Multiple choice

The sum of the age of a father and the age of his son is 75 years. If the product of their ages before 5 years was 750, then what is the present age of son?

  1. 30 years

  2. 55 years

  3. 25 years

  4. 20 years

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let present ages be f (father) and s (son). f + s = 75. Five years ago: (f-5)(s-5) = 750. Substituting f = 75-s: (70-s)(s-5) = 750. Expanding: 70s - 350 - s² + 5s = 750. Rearranging: s² - 75s + 1100 = 0. Solving: s = 25 or s = 44. But if s = 44, then f = 31 (impossible as father must be older). Thus s = 25. Checking: ages 5 years ago were 50 and 20, product = 1000, not 750. There's an error. Let son = 20, father = 55. Five years ago: 50 × 15 = 750. This works! Son is 20 years. Option D is correct.